Spanners of additively weighted point sets

Prosenjit Bose, Paz Carmi, Mathieu Couture

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p,r) where p is a point in the plane and r is a real number. The distance between two points (p i ,r i ) and (p j ,r j ) is defined as |p i p j |∈-∈r i ∈-∈r j . We show that in the case where all r i are positive numbers and |p i p j | ≥ r i ∈+∈r j for all i,j (in which case the points can be seen as non-intersecting disks in the plane), a variant of the Yao graph is a (1∈+∈ε)-spanner that has a linear number of edges. We also show that the Additively Weighted Delaunay graph (the face-dual of the Additively Weighted Voronoi diagram) has constant spanning ratio. The straight line embedding of the Additively Weighted Delaunay graph may not be a plane graph. Given the Additively Weighted Delaunay graph, we show how to compute a plane embedding with a constant spanning ratio in O(nlogn) time.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2008 - 11th Scandinavian Workshop on Algorithm Theory, Proceedings
Pages367-377
Number of pages11
DOIs
StatePublished - 27 Oct 2008
Externally publishedYes
Event11th Scandinavian Workshop on Algorithm Theory, SWAT 2008 - Gothenburg, Sweden
Duration: 2 Jul 20084 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5124 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Scandinavian Workshop on Algorithm Theory, SWAT 2008
Country/TerritorySweden
CityGothenburg
Period2/07/084/07/08

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